Cubic interaction vertex of higher-spin fields with external electromagnetic field

We fulfill the detailed analysis of coupling the charged bosonic higher-spin fields to external constant electromagnetic field in first order in external field strength. Cubic interaction vertex of arbitrary massive and massless bosonic higher-spin fields with external field is found. Construction is based on deformation of free Lagrangian and free gauge transformations by terms linear in electromagnetic field strength. In massive case a formulation with Stueckelberg fields is used. We begin with the most general form of deformations for Lagrangian and gauge transformations, admissible by Lorentz covariance and gauge invariance and containing some number of arbitrary coefficients, and require the gauge invariance of the deformed theory in first order in strength. It yields the equations for the coefficients which are exactly solved. As a result, the complete interacting Lagrangian of arbitrary bosonic higher-spin fields with constant electromagnetic field in first order in electromagnetic strength is obtained. Causality of massive spin-2 and spin-3 fields propagation in the corresponding electromagnetic background is proved.     

Lagrangian and Hamiltonian formalisms for relativistic dynamics of a charged particle with dipole moment

The Lagrangian and Hamiltonian formulations for the relativistic classical dynamics of a charged particle with dipole moment in the presence of an electromagnetic field are given. The differential conservation laws for the energy-momentum and angular momentum tensors of a field and particle are discussed. The Poisson brackets for basic dynamic variables, which form a closed algebra, are found. These Poisson brackets enable us to perform the canonical quantization of the Hamiltonian equations that leads to the Dirac wave equation in the case of spin 1/2. It is also shown that the classical limit of the squared Dirac equation results in equations of motion for a charged particle with dipole moment obtained from the Lagrangian formulation. The inclusion of gravitational field and non-Abelian gauge fields into the proposed formalism is discussed.Received: 4 June 2005, Published online: 27 July 2005     

Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators.     

The Relativistic Dynamics of the Combined Particle–Field System in Renormalized Classical Electrodynamics

This paper develops a general theory for the nonlinear, renormalized interaction between charged particles and electromagnetic fields. For the combined “particle + field” system, a fundamental relativistically invariant dynamical equation is derived from first principles. This theory was first obtained in an alternative way by one of us (J.K.) in an earlier paper. Here, we prove that the initial-value problem for the “particle + field” system is well-posed. The existence and uniqueness result is based on a careful analysis of the singularites of the electromagnetic field along the trajectory of the moving charged particle. Furthermore, the Banach fixed-point principle is used. The theory improves the classical Dirac theory for the motion of electrons. In particular, it is shown how to deal with the Dirac paradox of runaway solutions. Received: 10 December 1997 / Accepted: 21 April 1998     

On a Dynamic Formulation of Deformations of the Space R_1^4

The equations alternative to those of dynamics of a point charged particle are derived. In this case, the holonomic vector field of a special type represents the momentum, and the symmetric tensor is the external field. A class of electromagnetic fields which can be mechanically interpreted in terms of deformation theory is also considered.     

也谈带电粒子在电磁场中动态受力平衡条件

电磁场中相对论带电粒子的经典轨道运动受到洛伦兹力和辐射阻尼力的影响,在一定条件下会达到受力平衡状态．基于洛伦兹一狄拉克方程,本文介绍了计及辐射阻尼力后电磁场中带电单粒子(包括导体中的自由电子)受力平衡条件的一种可能的相对论协变形式．     

Quantum processes in short and intensive electromagnetic fields

This work provides an overview of our recent results in studying two most important and widely discussed quantum processes: electron-positron pairs production off a probe photon propagating through a polarized short-pulsed electromagnetic (e.g. laser) wave field or generalized Breit–Wheeler process, and a single a photon emission off an electron interacting with the laser pules, so-called non-linear Compton scattering. We show that the probabilities of particle production in both processes are determined by interplay of two dynamical effects, where the first one is related to the shape and duration of the pulse and the second one is non-linear dynamics of the interaction of charged fermions with a strong electromagnetic field. We elaborate suitable expressions for the production probabilities and cross sections, convenient for studying evolution of the plasma in presence of strong electromagnetic fields.     

The post-post-Newtonian problem in classical electromagnetic theory

We find the Lagrangian to order c^?4 for two charged bodies (with $\text{e}{}_1\text{m}{}_1\text{=}\text{e}{}_2\text{m}{}_2$) in electromagnetic theory. This Lagrangian contains acceleration terms in its final form and we show why it is incorrect to eliminate these terms by using the equationsof motion in the Lagrangian as was done by Golubenkov and Smorodinskii, and by Landau and Lifshitz. We find the center of inertia and show that the potential energy term does not split equally between particles 1 and 2 as it does in the Darwin Lagrangian (Lagrangian to order c^?2). In addition to the infinite self-energy terms in the electromagnetic energy-momentum tensor, which are eliminated using Gupta's method, some new type of divergent terms are found in the moment of electromagnetic field energy and in the electromagnetic field momentum which cancel in the final conservation law for the center of inertia.     

Radiation of de-excited electrons at large times in a strong electromagnetic plane wave

The late time asymptotics of the physical solutions to the Lorentz–Dirac equation in the electromagnetic external fields of simple configurations–the constant homogeneous field, the linearly polarized plane wave (in particular, the constant uniform crossed field), and the circularly polarized plane wave–are found. The solutions to the Landau–Lifshitz equation for the external electromagnetic fields admitting a two-parametric symmetry group, which include as a particular case the above mentioned field configurations, are obtained. Some general properties of the total radiation power of a charged particle are established. In particular, for a circularly polarized wave and constant uniform crossed fields, the total radiation power in the asymptotic regime is independent of the charge and the external field strength, when expressed in terms of the proper-time, and equals a half the rest energy of a charged particle divided by its proper-time. The spectral densities of the radiation power formed on the late time asymptotics are derived for a charged particle moving in the external electromagnetic fields of the simple configurations pointed above. This provides a simple method to verify experimentally that the charged particle has reached the asymptotic regime.     

Gravitation,Electromagnetism and Cosmological Constant in Purely Affine Gravity

The Ferraris-Kijowski purely affine Lagrangian for the electromagnetic field, that has the form of the Maxwell Lagrangian with the metric tensor replaced by the symmetrized Ricci tensor, is dynamically equivalent to the metric Einstein-Maxwell Lagrangian, except the zero-field limit, for which the metric tensor is not well-defined. This feature indicates that, for the Ferraris-Kijowski model to be physical, there must exist a background field that depends on the Ricci tensor. The simplest possibility, supported by recent astronomical observations, is the cosmological constant, generated in the purely affine formulation of gravity by the Eddington Lagrangian. In this paper we combine the electromagnetic field and the cosmological constant in the purely affine formulation. We show that the sum of the two affine (Eddington and Ferraris-Kijowski) Lagrangians is dynamically inequivalent to the sum of the analogous (ΛCDM and Einstein-Maxwell) Lagrangians in the metric-affine/metric formulation. We also show that such a construction is valid, like the affine Einstein-Born-Infeld formulation, only for weak electromagnetic fields, on the order of the magnetic field in outer space of the Solar System. Therefore the purely affine formulation that combines gravity, electromagnetism and cosmological constant cannot be a simple sum of affine terms corresponding separately to these fields. A quite complicated form of the affine equivalent of the metric Einstein-Maxwell-Λ Lagrangian suggests that Nature can be described by a simpler affine Lagrangian, leading to modifications of the Einstein-Maxwell-ΛCDM theory for electromagnetic fields that contribute to the spacetime curvature on the same order as the cosmological constant.     

Unified equation of motion of a test charge in electromagnetic and gravitational fields

This work starts by generalizing in a gravitational field the fundamental quantum mechanical commutation relations between the coordinates of a charged test particle and its momentum. Assuming that the components of the momentum of this test charge obey a noncommutative algebra in the presence of an electromagnetic field, it is proved that the commutator can be identified with the electromagnetic field tensor. Using these results, the equation of motion of this charged object in the presence of both the electromagnetic and gravitational fields is derived from their field equations. In this work, the laws of motion of a particle in the electromagnetic and gravitational fields has been unified with the field equations. Although the field equations themselves are not directly unified, this work strongly suggests that the scheme may act as a possible framework for the unification of at least gravitational and electromagnetic interactions.     

Random Motion of a Charged Test Particle with a Constant Classical Velocity in a Spacetime with a Plane Boundary

We study the random motion of a charged test particle coupled to electromagnetic vacuum fluctuations near a perfectly reflecting plane boundary with a nonzero classical constant velocity in a direction parallel to the plane. We calculate the mean squared fluctuations in the velocity and position of the test particle taking into account both fluctuating electric and magnetic forces. Our results show that the influence of fluctuating magnetic fields is, in general, of the higher order than that caused by fluctuating electric fields and is thus negligible.     

The Bargmann-Wigner method in Galilean relativity

The equations of motion of a spin one particle as derived from Levy-Leblond's Galilean formulation of the Bargmann-Wigner equations are examined. Although such an approach is possible for the case of free particles, inconsistencies which closely parallel those encountered in the Bargmann-Wigner equations of special relaticity are shown to occur upon the introduction of minimal electromagnetic coupling. If, however, one considers the vector meson within the Lagrangian formalism of totally symmetric multispinors, it is found that the ten components which describe the vector meson in Minkowski space reduce to seven for the Galilean group and that in this formulation no difficulty occurs for minimal electromagnetic coupling.More generally it is demonstrated that one can replace Levy-Leblond's version of the Bargmann-Wigner equations by an alternative set which leads to the correct number of variables for the vector meson. A final extension consists in the proof that for all values of the spin the (Lagrangian) multispinor formalism implies the Bargmann-Wigner equations. Thus the problem of special relativity of seeking a Lagrangian formulation of the Bargmann-Wigner set is found to have only a somewhat trivial counterpart in the Galilean case.Research supported in part by the U.S. Atomic Energy Commission.     

Is there a preferred canonical quantum gauge?

The interaction between a long solenoid and a charged particle in the field free region outside it is studied treating both systems quantum mechanically. This leads to a paradox which suggests that when the electromagnetic field is quantized, there may be a preferred quantum gauge for the vector potential. This paradox is resolved by canonically quantizing the system in a different gauge in which the classical Lagrangian or Hamiltonian contains an acceleration dependent term.     

On electromagnetic waves by an accelerated charged particle in medium

We have investigated the effects of acceleration of a charged particle on its Cerenkov emission and ionization-losses. We have considered the accelerated motion of a charged particle in an infinite medium with the acceleration parallel to the direction of its motion. We have used the method of Fourier transforms to solve the Maxwell's equations with appropriate current and charge-densities to find electromagnetic fields and hence the force experienced by the incident charge due to its interaction with the medium (dielectric or plasma). The results obtained are general and applicable to any acceleration. In the approximations of ‘small acceleration’ and ‘small interaction time’, we have solved the wave equations and determined electromagnetic potentials. It is found that the acceleration of the charged particle strongly changes both its ionization-loss and Cerenkov emission.     

On the Electromagnetic Origin of Inertia and Inertial Mass

We address the problem of inertial property of matter through analysis of the motion of an extended charged particle. Our approach is based on the continuity equation for momentum (Newton’s second law) taking due account of the vector potential and its convective derivative. We obtain a development in terms of retarded potentials allowing an intuitive physical interpretation of its main terms. The inertial property of matter is then discussed in terms of a kind of induction law related to the extended charged particle’s own vector potential. Moreover, it is obtained a force term that represents a drag force acting on the charged particle when in motion relatively to its own vector potential field lines. The time rate of variation of the particle’s vector potential leads to the acceleration inertia reaction force, equivalent to the Schott term responsible for the source of the radiation field. We also show that the velocity dependent term of the particle’s vector potential is connected with the relativistic increase of mass with velocity and generates a longitudinal stress force that is the source of electric field lines deformation. In the framework of classical electrodynamics, we have shown that the electron mass has possibly a complete electromagnetic origin and the obtained covariant equation solves the “4/3 mass paradox” for a spherical charge distribution.     

空间对称性与电磁角动量守恒

阐明空间对称性与守恒律，并结合电磁场中带电粒子的拉氏函数，巧妙简捷地处理了一个电磁系统的角动量守恒。